Staff profile

I completed my PhD in Applied Mathematics at Dublin City University in 2018. I was then a postdoctoral researcher in the Mathematics Department at Brandeis University with Prof. Jonathan Touboul. Subsequently, I joined the High Meadows Environmental Institute and Prof. Simon Levin’s lab at Princeton University. In August 2023, I joined the Department of Mathematical Sciences in the Applied Mathematics Group.

In my doctoral work, I studied qualitative properties of nonlinear differential systems with memory and subject to random noise. In my postdoctoral work, I expanded my research interests to include applications of techniques from dynamical systems and stochastic analysis to problems in ecology (savanna-forest modelling), developmental biology (cell fate dynamics in the brain), and epidemiology (malaria immune dynamics).

Currently, I'm working on mathematical problems related to understanding the movement of forest-savanna boundaries, within-host malaria dynamics, and coexistence in microbial ecosystems.

Teaching

I lecture the Michaelmas term of the 4H/Masters-level course "Advanced Mathematical Biology" at Durham. More details on courses I've taught and my teaching philosophy are available on my teaching page. 

I’m always open to discussing potential summer research opportunities with motivated students, and my students have been supported by London Mathematical Society and Biophysical Sciences Institute Bursaries in the past. Please get in touch with me if you are interested in a summer project on topics related to my research.

• Mathematical biology, dynamical systems, (nonlocal) PDEs, stochastic processes, mathematical modelling.

Journal Article

• Patterson, D., Levin, S., Staver, A. C., & Touboul, J. (2024). Pattern Formation in Mesic Savannas. Bulletin of Mathematical Biology, 86(1), https://doi.org/10.1007/s11538-023-01231-7
• Patterson, D. D., Staver, A. C., Levin, S. A., & Touboul, J. D. (2023). Spatial Dynamics with Heterogeneity. SIAM Journal on Applied Mathematics, S225-S248. https://doi.org/10.1137/22m1509850
• Qu, Z., Patterson, D., Childs, L. M., Edholm, C. J., Ponce, J., Prosper, O., & Zhao, L. (2023). Modeling Immunity to Malaria with an Age-Structured PDE Framework. SIAM Journal on Applied Mathematics, 83(3), 1098-1125. https://doi.org/10.1137/21m1464427
• Xu, L., Patterson, D., Levin, S. A., & Wang, J. (2023). Non-equilibrium early-warning signals for critical transitions in ecological systems. Proceedings of the National Academy of Sciences, 120(5), Article e2218663120. https://doi.org/10.1073/pnas.2218663120
• Feng, J., Hsu, W., Patterson, D., Tseng, C., Hsing, H., Zhuang, Z., …Chou, S. (2021). COUP-TFI specifies the medial entorhinal cortex identity and induces differential cell adhesion to determine the integrity of its boundary with neocortex. Science Advances, 7(27), Article eabf6808. https://doi.org/10.1126/sciadv.abf6808
• Xu, L., Patterson, D., Staver, A. C., Levin, S. A., & Wang, J. (2021). Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach. Proceedings of the National Academy of Sciences, 118(24), Article e2103779118. https://doi.org/10.1073/pnas.2103779118
• Patterson, D. D., Levin, S. A., Staver, C., & Touboul, J. D. (2020). Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications. SIAM Journal on Applied Dynamical Systems, 19(4), 2682-2719. https://doi.org/10.1137/19m1298329